Stability of solution sets for parametric set-valued optimization problems

MENG Xudong

doi:10.13471/j.cnki.acta.snus.ZR20250123

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Stability of solution sets for parametric set-valued optimization problems

Research articles | 更新时间：2025-11-14

- Stability of solution sets for parametric set-valued optimization problems
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 5, Pages: 154-162(2025)
- 作者机构：
  
  南昌航空大学科技学院，江西共青城 332020
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20250123
  CLC： O221.3
- Received：08 July 2025，
  
  Revised：2025-08-19，
  
  Accepted：25 August 2025，
  
  Published Online：17 September 2025，
  
  Published：25 September 2025
- 稿件说明：
移动端阅览
孟旭东.参数集值优化问题解集的稳定性[J].中山大学学报(自然科学版)(中英文),2025,64(05):154-162.

MENG Xudong.Stability of solution sets for parametric set-valued optimization problems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(05):154-162.
孟旭东.参数集值优化问题解集的稳定性[J].中山大学学报(自然科学版)(中英文),2025,64(05):154-162. DOI： 10.13471/j.cnki.acta.snus.ZR20250123.

MENG Xudong.Stability of solution sets for parametric set-valued optimization problems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(05):154-162. DOI： 10.13471/j.cnki.acta.snus.ZR20250123.

摘要

在赋范线性空间中研究了参数集值优化问题解集的稳定性. 首先，给出了参数集值优化问题

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3.89466691

-最小解映射和弱

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2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006451&type=

3.89466691

-最小解映射的概念及其关系. 其次，运用分析方法讨论了参数集值优化问题

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006465&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006451&type=

3.89466691

-最小解映射和弱

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006465&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006451&type=

3.89466691

-最小解映射的上半连续性和解集的紧性. 最后，借助水平集值映射获得了参数集值优化问题

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006465&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006451&type=

3.89466691

-最小解映射和弱

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006465&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006451&type=

3.89466691

-最小解映射的下半连续性定理，并给出例子解释了所得结果的有效性.

Abstract

The stability of solution sets for parametric set-valued optimization problems is studied in normed vector space. Firstly， the concepts about

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2.62466669

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4.57200003

-minimal solution mapping and weak

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-minimal solution mapping for parametric set-valued optimization problems and their relations are given. Secondly， using analytical method， upper semicontinuity and compactness of

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2.62466669

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4.57200003

-minimal solution mapping and weak

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-minimal solution mapping to parametric set-valued optimization problems are discussed. Finally， the lower semicontinuity theorems for

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2.62466669

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4.57200003

-minimal solution mapping and weak

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-minimal solution mapping of parametric set-valued optimization problems are obtained by the level set-valued mapping. Some examples are given to explain effectiveness of the obtained results.

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references

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